Single Linear-bivariate Cubic Systems (Series on Complexity, Nonlinearity and Chaos)

This book is about the nonlinear dynamics of single linear-bivariate cubic dynamical systems. For such cubic dynamical systems, the inflection-flows and third-order parabola flows exist for appearing bifurcations. The inflection-flows are for appearing bifurcations of two parabola flows on the same direction. The third-order parabola flows are for the appearing bifurcation of inflection and parabola flows, and for the appearing bifurcations of up, down and up-parabola flows or down, up and down-parabola flows. Third-order parabola flow are for the appearing bifurcation among the up and down-parabola flows. There are four types of infinite-equilibriums: (i) The inflection-source and sink infinite-equilibriums are for the switching bifurcations of two parabola flows on the two-directions. (ii) The parabola-source and sink infinite-equilibriums are for the switching bifurcations of parabola and inflection flows on the two-directions. (iii) The inflection-saddle infinite-equilibriums are for the switching bifurcation of two inflection flows in two directions. (iv) The parabola-saddle infinite-equilibriums are for the switching bifurcations of parabola and inflection flows on the two-directions are the switching bifurcations for parabola and inflection flows. Such switching bifurcations for 1-dimensional flow are based on the infinite-equilibriums, which will help one understand global dynamics in nonlinear cubic systems.

Professor Albert C J Luo is a Distinguished Research Professor at the Department of Mechanical and Mechatronics Engineering of Southern Illinois University at Edwardsville. For over 30 years, Dr Luo's contributions on nonlinear dynamical systems and mechanics lie in (i) the local singularity theory for discontinuous dynamical systems, (ii) dynamical systems synchronization, (iii) analytical solutions of periodic and chaotic motions in nonlinear dynamical systems, (iv) the theory for stochastic and resonant layer in nonlinear Hamiltonian systems, and (v) the full nonlinear theory for a deformable body. Such contributions have been scattered into over 50 monographs and over 400 peer-reviewed journal and conference papers. Dr Luo served editors for the Journal Communications in Nonlinear Science and Numerical simulation, book series on Nonlinear Physical Science (HEP) and Nonlinear Systems and Complexity (Springer). Dr Luo was the editorial member for two journals (i.e., Proc. Inst. Mech. Eng. K: Journal of Multibody Dynamics and Journal of Vibration and Control). He is currently an associate editor for International Journal of Bifurcation and Chaos and AIP Chaos. He also organized over 30 international symposiums and conferences on Dynamics and Control.